Wireless Energy Transfer Using Arrays of Resonant Objects

ABSTRACT

A system for exchanging energy wirelessly includes an array of at least three objects, wherein the objects have similar resonant frequencies, wherein each object is electromagnetic (EM) and non-radiative and generates an EM near-field in response to receiving the energy. Each object is electrically isolated from the other objects and arranged at a distance from all other objects, such that upon receiving the energy, the object is strongly coupled to at least one other object via a resonant coupling of evanescent waves. An energy driver provides the energy at the resonant frequency to at least one object in the array, such that, during an operation of the system, the energy is distributed from the at least one object to all other objects in the array via the resonant coupling of the evanescent waves.

RELATED APPLICATIONS

The present invention claims priority to U.S. Provisional Patent Application 61/447599, “Wireless Energy Transfer Using Array of Resonant Objects,” filed by Wang et al. on Feb. 28, 2011, and is related to U.S. Patent Applications (MERL-2421), “Tuning electromagnetic fields characteristics for wireless energy transfer using arrays of resonant objects,” co-filed herewith by Wang et al. on ______, 2011, and U.S. Patent Application (MERL-2429) “System and method for automatically optimizing wireless power, co-filed by Yerazunis et al, on ______, 2011, all incorporated herein by reference.

FIELD OF THE INVENTION

This invention relates generally to transferring energy wirelessly, and more particularly to transferring energy using an array of resonant objects.

BACKGROUND OF THE INVENTION

Wireless Energy Transfer

Inductive coupling is used in a number of wireless energy transfer systems, such as a cordless electronic toothbrush, or vehicle batteries. In coupled inductors, such as transformers, a source, e.g., a primary coil, generates energy as an electromagnetic field, and a sink, e.g., a secondary coil, arranged in the so that the energy passing through the energy sink is optimized, e.g., the energy generated by the sink is as similar as possible to the energy of the source. To optimize the energy, a distance between the source and the sink should be as small as possible, because over greater distances the inductive coupling method is ineffective.

Resonant Coupling System

FIG. 1 shows a conventional resonant coupling system 100 for transferring energy from a source 110 to a sink 120. In resonant coupling, two resonant electromagnetic objects, i.e., the source and the sink, interact with each other under resonance conditions.

A driver 140 inputs the energy into the source to form an electromagnetic field 115. The electromagnetic field attenuates at a rate with respect to the excitation signal frequency at driver or self-resonant frequency of source and sink for a resonant system. However, if the sink absorbs more energy than is lost during each cycle, then most of the energy is transferred to the sink. Operating the source and the sink at the same resonant frequency ensures that the sink has a lower impedance at that frequency, and that the energy is optimally absorbed.

The energy is transferred, over a distance D, between resonant objects, e.g., the source has a length L₁ and the sink has a length L₂. The driver connects a power provider to the source. The sink is connected to a power consuming device, e.g., a resistive load 150. Energy is supplied by the driver to the source, transferred wirelessly and non-radiatively to the sink, and consumed by the load. The wireless non-radiative energy transfer is performed using the field 115, e.g., the electromagnetic field or an acoustic field of the resonant system. For simplicity of this description, the field 115 is an electromagnetic field. During the coupling of the resonant objects, evanescent waves 130 are propagated between the source and the sink.

However, the resonant coupling transfers energy from the source to the sink over a mid-range distance, e.g., a few times of the resonant frequency wavelength, inefficient when the distance becomes greater. It is thus desirable to extend the range of efficient wireless energy transfer.

Resonator Arrays

Resonator arrays have been used in the prior art for energy transfer. The rational behind conventional arrays is to produce a larger resonator by manufacturing and combining smaller resonators. Accordingly, the resonators in the conventional arrays are electrically interconnected with each other to form larger composite” resonator.

In another array, there is a set of four tuned circuits in the system, i.e., tuned transmitting antenna, transmitting resonant coil, receiving resonant coil, tuned receiving antenna. There can be more than one receiving devices, each with tuned receiving circuits, to receive energy from the transmitter.

SUMMARY OF THE INVENTION

The embodiments of the invention use an array of strongly coupled resonant objects to extend a range of efficient wireless energy transfer, and facilitate an energy transfer to mobile receiving objects.

If the energy is provided to at least one object of an array of strongly coupled resonant objects, the energy oscillates among all objects in the array with reasonable losses. If the energy is provided to at least one object in the array, then the energy is distributed from the object to all other objects in the array. Thus, an energy sink can receive energy wirelessly from any object of the array. Accordingly, the embodiments of the invention provide a novel way to store and distribute energy for subsequent wireless retrieval of the energy at any desired direction and distance from an energy source.

In conventional energy distribution systems, the energy is transmitted over a closed loop to return the unused energy back to the energy source, or to other specially designed energy storages. That was not considered as a problem, but rather as a fact of the energy transfer. The embodiments of the invention eliminate this requirement by allowing arbitrarily arrangements of the objects, and thus, enabling arbitrarily configurations of energy distribution topography.

In one embodiment, a system configured to transfer energy wirelessly between a transmitting device and a receiving device is provided. The system comprises an energy source, which is formed by an array of resonant objects, to generate evanescent electromagnetic (EM) waves. The system further comprises an energy driver for providing the energy to at least one object in the array, such that, during an operation of the system, the energy is distributed, e.g., oscillated, from the object to all other objects in the array.

In one variation of this embodiment, the system further comprises an energy sink at a distance from the energy source for receiving energy wirelessly from the energy source via coupling of evanescent EM waves. The sink can be resonant or non-resonant structures. The energy transfer can be achieved from any resonant object in the array of the energy source.

Another embodiment discloses a system configured to exchange energy wirelessly, comprising: an energy source comprising a first array of objects; an energy sink comprising a second array of objects, each object in the energy source and energy sink has a resonant frequency, is electromagnetic (EM) and non-radiative, and is configured to generate an EM near-field in response to receiving the energy; an energy driver for providing the energy at the resonant frequency to at least one object in the energy source, such that, during an operation of the system, the energy is distributed from the object in the energy source to all other objects in the energy source; and a load from receiving the energy from the energy sink, wherein each object in the first and the second arrays is arranged at a distance from all other objects in, respectively, the first and the second arrays, such that upon receiving the energy the objects in the first and the second arrays are strongly coupled to, respectively, at least one other object in the first and the second array, via a resonant coupling of evanescent waves, and wherein the energy sink is arranged to receive energy wirelessly from the energy source via the resonant coupling of one or many objects in the first array with one or many objects in the second array. Therefore, as defined herein a strong coupling is due to a resonant coupling of evanescent waves,

In another embodiment, a method of transferring energy wirelessly between an energy source and an energy sink is disclosed. The method comprises generating evanescent EM waves in an array of resonant objects. The method further comprises transferring energy wirelessly between the array of resonant objects and an energy sink. The energy sink can be a resonant or non-resonant structure. In another embodiment, the method further comprises transferring the energy wirelessly between the array of resonant objects and another array of resonant objects.

Other embodiments use metamaterials and reflectors arranged near the array.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a conventional resonant coupling system;

FIG. 2 is a block diagram of a system with an energy sink beyond a range of efficient wireless energy transfer;

FIG. 3 is a block diagram of a system with a resonator array as an energy source according to embodiments of the invention;

FIGS. 4A-D are schematics of an array of strongly coupled resonant objects according to embodiments of the invention;

FIG. 5 is block diagram of a system for supplying energy wirelessly to moving objects according to embodiments of the invention;

FIGS. 6A-C are schematics comparing different implementations of an energy sink;

FIG. 7 is a block diagram of a system with a resonator array as the energy source and the energy sink according to embodiments of the invention;

FIG. 8 is block diagram of a system for supplying energy wirelessly to moving objects according to embodiments of the invention;

FIG. 9 is a schematic of an array of spiral operating resonators according to embodiments of the invention;

FIGS. 10A-E are graphs of transfer efficiency as a function of frequency in the resonant array system and corresponding resonant modes according to embodiments of the invention;

FIG. 11 is a schematic of a field intensity distribution pattern; and

FIG. 12 is a schematic of an example of one dimensional system extended to two dimensional plane systems according to embodiments of the invention;

FIG. 13 is a schematic of coordinate systems for wireless energy transfer:

FIGS. 14-15 are graphs of energy as a function of distance;

FIG. 16 is a schematic of a moving receiver along a linear array of resonant objects;

FIG. 17 is a schematic of two cases of receivers;

FIG. 18 is a graph of energy efficiency as a function of frequency;

FIG. 19 is a schematic of side views of two cases of energy transfer;

FIG. 20 is a schematic of side views of a moving receiver;

FIGS. 21A-21B are graphs of energy efficiency as a function of receiver position;

FIG. 22 is a schematic of two moving receivers moving along an array;

FIG. 23A-23B are graphs of energy efficiency as a function of receiver positions;

FIG. 24 is a schematic of a moving receiver and two arrays;

FIG. 25-26 are schematics of one and two arrays;

FIG. 27-28 are schematics of a metamaterial array and a moving receiver;

FIG. 29 is a schematic of energy loss from an array;

FIGS. 30-131 are schematics of arrays and reflectors; and

FIG. 32 is a graph of energy efficiency as a function of frequency.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Energy can be transferred wirelessly and efficiently between coupled resonant objects at a resonant frequency. When the size of resonant object is much smaller than the resonant wavelength, most of the energy is stored inside the resonant object and does not radiate. The range of efficient wireless energy transfer depends on the physical size of resonant objects. The energy transfer is inefficient when the receiving object moves over a large distance, compared to the size of resonant objects.

Thus, the resonant energy transfer system shown in FIG. 1 is efficient when the distance D is on the order of the energy source size L₁ and the energy sink size L₂. When D is much larger than the sizes L₁ or L₂, the energy transfer is inefficient. Moreover, depending on the structure design of source 110 and sink 120, the system usually requires alignment along one axis.

FIG. 2 shows an example when the wireless energy transfer using resonant energy source 210 coupled to an energy driver 230, and resonant energy sink 220 coupled to a load 240 is inefficient. The energy sink 220 is a distance D in the x direction and a distance L in the y direction from the energy source 210, where the distance L 250 is much larger than L₁ and L₂. Moreover, the sink 220 can move along a direction line 250. Thus, it is desirable to extend the range of efficient wireless energy transfer and design a system to provide energy wirelessly to mobile devices, such as elevators or electric vehicles.

The embodiments of the invention use an array of strongly coupled resonant objects to extend the range of efficient wireless energy transfer and facilitates an efficient energy transfer to receiving objects moving over a large distance.

Coupled Resonator Array

FIG. 3 shows a system 300 according to embodiments of the invention. Instead of using one resonant object as the energy source, an array of at least three resonant objects 311 having similar resonant frequencies is used as the source 310. For example, the frequencies do not vary more than a bout 10% of each other. Each object is electromagnetic (EM) and non-radiative, and configured to generate an EM near-field in response to receiving the energy. The array 310 can be any arrangement of the objects 311. The objects 311 in the array are arranged at a distance from each other. The objects are electrically isolated. As defined herein, electrically isolated means that there are no wired electrical conductors between any of the objects. However, the energy received by any object is strongly coupled to at least one other object in the array via resonant coupling of an electromagnetic wave 360.

It is noted that the resonant object, as shown in FIG. 3, and all other resonators described for the various embodiments are electrically isolated from each other, i.e. not connected by a physical conductor. Because the objects are not wired to each other, the arrangement of the object in the array can be quite arbitrary and flexible to serve various applications.

The type of resonant coupling in the array can be an inductive coupling, a capacitive coupling, or combination thereof. An energy driver 330 is used to provide energy to one or more objects in the array 310. Through the resonant coupling, the energy is distributed to all the objects in the array 310. The energy distribution in the array is achieved by the excitation of the evanescent waves that propagate along the objects of the array due to the resonant coupling. The evanescent wave is localized within the near-field of the resonant objects and does not radiate to free space. In one embodiment, to reduce the loss during the process, resonant objects with high quality factor (Q-factor, Q>100) are selected.

The Q factor is a dimensionless parameter that describes how under-damped the resonator is, or equivalently, characterizes a resonator's bandwidth relative to its center frequency. A higher Q indicates a lower rate of energy loss relative to the stored energy of the oscillator.

An energy sink 320 is a distance D from the array. The sink can be constructed as a resonant object or a non-resonant object. The energy is transferred from the source to the sink 320 via coupling of evanescent waves 370. The coupling can occur between one or more objects in the source and the sink. The sink receives energy wirelessly from the source and provides energy to a load 340. The sink can be at different locations along the line 350. Different objects in the source 310 are coupled to the sink 320 when the energy sink is at different locations.

Embodiments of the invention provide the energy to at least one object of an array of strongly coupled resonant objects, the energy oscillates among all objects in the array with reasonable losses. If the energy is provided to at least one object in the array, then the energy is distributed from the object to all other objects in the array. Thus, the energy sink can receive energy wirelessly from any object of the array. Accordingly, the embodiments of the invention provide a way to store and distribute energy for subsequent wireless retrieval of the energy at any desired direction and distance from the energy driver.

In conventional energy distribution systems, the energy is transmitted over a closed loop to return unused energy to the energy source or to other specially design energy storages. That was not considered as a problem, but rather as a fact of the energy transfer. The embodiments of the invention eliminate this requirement and allow arbitrarily arrangements of the objects and thus, arbitrarily configuration of energy distribution topography.

Array Configurations

The resonant object 311 in the resonant array 310 can take any physical shape depending on the application. For example, the resonant object can be self resonant coils, spirals, and dielectric resonators.

In one embodiment as shown in FIG. 4A, the resonant object has the form of a planar spiral 411. The resonant object can form different arrangement forming the array of different shapes. An array 410 is formed by linearly arranging multiple resonant objects. The spiral object 411 is made of conducting wires and is self-resonant at the resonant frequency. The sink can include one or more objects constructed with resonant or non-resonant structures. In one embodiment, the sink is constructed by the spiral 420, and arranged on top of one of the objects of the array 410. In another embodiment, the sink is movable between a current and another location 430. In yet another embodiment, multiple sinks 420 and 430 are used at different locations.

FIGS. 4B-D show more complex shapes of the array. FIG. 4B shows an array 440 of resonant objects arranged a curve. In another embodiment as shown in FIG. 4C, the resonant objects are arranged along a circle 450. In yet another embodiment as shown in FIG. 4D, the resonant objects can be arranged in two dimensions in a plane 460. In various embodiments, the sink is a resonant object having the resonant frequency for receiving the energy wirelessly.

EXAMPLE APPLICATIONS

The embodiments of the invention can be applied to various applications to provide energy wirelessly to mobile devices, or wirelessly charge batteries on different devices. The devices include, but are not limited to, electric vehicles, elevators, robots, electronic devices such as cell phones, laptops.

FIG. 5 shows a system 500 for providing the energy wirelessly to an elevator car 550. The source is formed by an array 510 of resonant objects 511, and is installed in an elevator shaft. A driver 530 is used to provide energy to one or more objects in the array 510. The driver 530 is connected to a power source. The sink 520 is a resonant object, and connected to a load 540 of the elevator for powering the elevator car. The sink 520, at a distance D from the array, receives energy wirelessly from the energy source, and provides energy to the load 540. Both the sink 520 and the load 540 are positioned outside of the elevator car 550. Impedance matching networks and other components (not shown) can be used to control and optimize the performance of the elevator system. The system can be adapted to other applications such as wireless charging of electric vehicles.

Resonator Array as Energy Sink

Some embodiments of the invention use a sink formed by an array of resonators. FIGS. 6A-6B show examples of systems 610 and 620 having different configurations. In both systems, the energy source is constructed by spirals aligned in a linear array. A loop antenna is used at the driver to provide energy to the resonant spiral at one end of the array. In the system 610, the sink is an identical spiral resonator and is aligned coaxial with the resonant spiral at the other end of the array. The sink is 0.5 m from the plane of the array. The load is 0.1 m from the driver. A loop antenna is used to extract energy from the energy sink. In system 620, the energy sink is constructed by an array of identical spirals. A loop antenna is aligned coaxial with the spiral at one end of the array.

FIG. 6C shows that the transfer efficiency 625 as a function of frequency of the system 620 is better than the transfer efficiency 615 in the system 610.

Two Coupled Resonator Arrays

FIG. 7 shows a system 700 including a pair of resonator arrays, i.e., a first array 710 and a second array 720, for wireless energy transfer. The field oscillating at a resonant frequency is provided to the source 710 from the drive 730. The energy can be provided wirelessly. The energy source 710 and the sink 720 are arrays of resonant objects 711 and 721. Mutual coupling between the resonant objects in the energy source and the energy sink redistributes the wireless energy in the system according to the resonant arrays configuration. Typically, the distance between objects of, respectively, the first and the second arrays, is less than a distance between the energy source and the energy sink.

The mutual coupling between the arrays 710 and 720 supports the wireless energy transfer through the near field 750 over mid-range, e.g., several resonant object dimension size. The energy is transferred from the energy source to the energy sink via coupling of one or more resonant objects in the energy source with one or more resonant objects in the energy sink. The overall filed distribution due to the mutual coupling forms a coupled mode of the two resonator arrays of a single system.

In various embodiments, the resonant objects 711 and 721 are of different shape and geometry. The resonant frequency can vary between the energy source and the energy sink. However, one embodiment maintains the same resonant frequency for both resonant objects to achieve the optimum energy transfer efficiency.

In various embodiments, a size of the first array is less, greater, or equal a size of the second array. The first and the second arrays can be of the same or different dimensions. The first and the second arrays can have the same or different degrees of freedom. In one embodiment, the second array has at least one degree of freedom.

In some embodiment, the driver can provide energy to one or to several resonant objects concurrently. Also, in one embodiment, a driver feeding position 731 can move. The system resonating frequencies and the resonant mode for each resonant frequency are fixed after the system configuration, i.e., the objects of the energy source and the energy sink, are determined. The driver 730 can provide energy to the system at any resonator object 711 in the energy source 710.

Similarly, in one embodiment, the load energy extraction position can move. The energy can be extracted from any resonant object 721 of the energy sink. In variation of this embodiment, the load 740 can extract energy from more than one object in the array of the energy sink, e.g., at different positions 741-744.

In some embodiments, multiple drivers in the system 700 can be used to provide energy to the energy source array 710 at different positions. Similarly, multiple loads 740 and 745 can be used to extract energy from the energy sink 720 at different positions.

Mobile Device

FIG. 8 shows a system 800 for supplying energy wirelessly to moving devices, such as elevator cars. The energy source is an array 860 of resonant objects 880. The energy source is installed at in an elevator shaft and receives energy 815 from an energy driver 810. The energy driver can be connected to a power grid and supply energy to the energy source, e.g., inductively. The resonator array is configured to generate electromagnetic evanescent waves in the specified resonant mode at specified resonant frequency.

The elevator car 850, i.e., the load, is connected wirelessly to the energy sink formed by a resonator array 820. The energy sink can have less, more or the same number of resonant objects as the resonator array of the energy source.

Example

FIG. 9 shows another example embodiment. Spiral resonators 910 resonating at 27 MHz form the resonator arrays of the energy source 920 and the energy sink 930. For example, both resonator arrays have 6 spiral elements. Two loop antennas with R radius are used as the energy driver 940 and the load 950.

The separation between driver/load and source array/sink array is D2. The distance between the energy source and sink array is D.

For example, the energy is provided to the driver via wired cable and then provided to the source via, e.g., inductive coupling at resonant frequency. The specified resonant mode is excited in the system and the energy redistributed over the whole system according to the resonant mode. The load 950 extracts the energy wireless out of the system from the energy sink 930. When the energy is extracted from the system, energy balance of the system is disturbed and more energy is provided from the driver to maintain the balance. Accordingly, the energy transferred from drive to load continues as long as the resonant mode is maintained in the system.

Because the resonant mode of the system is frequency dependent, the transfer efficiency is also frequency dependent, as shown in FIG. 10A. The energy transfer efficiency 1030 has multiple peaks in the system which is the result of the multiple resonator configurations.

Different peaks in the power transfer efficiency curve, 1011-1014, correspond to different corresponding resonant modes 1021-1024 as shown in FIGS. 10B-10E. When the resonant mode common to the whole system is excited, the energy is confined within the system with little radiation.

In particular, the highest power transfer efficiency from the driver to the load is at the resonant mode where the energy is evenly distributed over the all system, which is the peak 1014.

FIG. 11 shows the corresponding mode 1110. Each resonator in the source 920 and the sink 930 are excited in this resonant mode, and the energy is evenly distributed oscillating along and between the two arrays.

Two-Dimensional Resonant Arrays

FIG. 12 shows how the array of resonant objects can have different dimensions, e.g., a two-dimensional (2D) array of the resonant objects. The 2D arrays extending in both the x and y direction, and is used as the energy source 1240 and the energy sink 1230. The energy driver 1260 provides 1250 the energy to the source at the resonant frequency. Due to the mutual coupling, 1270-1273, between the resonant objects in the source, wireless energy redistributed over the system in both direction. The mutual coupling 1274 between the resonant objects in the sources and the resonant objects in the sink results in the wireless energy transfer from the source 1240 to the sink 1230. The corresponding resonant mode of the overall system is excited through the providing energy at the resonant frequency. At the corresponding resonant mode, the energy in the system 1200 is redistributed in three directions, Particularly, the energy is transferred wirelessly in the z direction.

Coupling of Two Loops of Metallic Wires

Coupling of electromagnetic (EM) waves is essential in wireless power transfer based on inductive coupling and resonant coupling. It is important to understand the coupling behavior between EM objects to better design a wireless power transfer system.

We first describe into the coupling of two loops of metallic wires. FIG. 13 shows two coupled metallic loops. The positions and geometrical parameters of them are defined in the coordinate system. The mutual coupling of two metallic loops can be described by,

${M = {{\Phi/I_{1}} = {\frac{\mu_{0}}{4\pi}R_{1}R_{2}{\int_{0}^{2\pi}{\int_{0}^{2\pi}{\frac{\left( {{\sin \; \varphi_{1}\sin \; \varphi_{2}} + {\cos \; \varphi_{1}\cos \; \varphi_{2}\cos \; \theta}} \right)}{r}\ {\varphi_{1}}\ {\varphi_{2}}}}}}}},$

where Φ is the magnetic flux going through the second loop due to the electric current I₁ in the first loop, and

$r = {{{{\overset{\rightarrow}{x}}_{A} - {\overset{\rightarrow}{x}}_{B}}} = {\sqrt{\begin{matrix} {\left( {{R_{1}\cos \; \varphi_{1}} - {R_{2}\cos \; \varphi_{2}}} \right)^{2} +} \\ {\left( {{R_{1}\sin \; \varphi_{1}} - t - {R_{2}\sin \; \varphi_{2}\cos \; \theta}} \right)^{2} + \left( {d - {R_{2}\sin \; \varphi_{2}\sin \; \theta}} \right)^{2}} \end{matrix}}.}}$

The self-inductance of the two loops are L₁ and L₂. The coupling coefficient is defined as k=M/√{square root over (L₁L₂)}. The self-inductance of a metallic loop with radius R is

$L = {\mu_{0}{{R\left\lbrack {{\ln \left( \frac{8\; R}{a} \right)} - 2} \right\rbrack}.}}$

Next we consider two special cases of two loops with identical size, with self-inductance L₂=L₂. These two cases are shown in FIGS. 14-15.

When the two loops are co en in FIG. 14, with distance d between them, the equations are simplified:

$\begin{matrix} {r = \sqrt{\left( {{R_{1}\cos \; \varphi_{1}} - {R_{2}\cos \; \varphi_{2}}} \right)^{2} + \left( {{R_{1}\sin \; \varphi_{1}} - {R_{2}\sin \; \varphi_{2}}} \right)^{2} + d^{2}}} \\ {{= \sqrt{R_{1}^{2} + R_{2}^{2} - {2\; R_{1}R_{2}{\cos \left( {\varphi_{1} - \varphi_{2}} \right)}} + d^{2}}},} \end{matrix}$ $M = {\frac{\mu_{0}}{4\pi}R_{1}R_{2}{\int_{0}^{2\pi}{\int_{0}^{2\pi}{\frac{\cos \left( {\varphi_{1} - \varphi_{2}} \right)}{\sqrt{R_{1}^{2} + R_{2}^{2} - {2\; R_{1}R_{2}{\cos \left( {\varphi_{1} - \varphi_{2}} \right)}} + d^{2}}}{\varphi_{1}}\ {{\varphi_{2}}.}}}}}$

The coupling coefficient is calculated numerically (and plotted as a function of distance in FIG. 14. The coupling coefficient is very strong at short range, when the two loops are close to each other. When the distance is equal to the radius of loop, the coupling coefficient k decreases to about 0.05.

When the two loops are coplanar, as seen in FIG. 15, with distance d between them, the equations are simplified:

$\begin{matrix} {r = \sqrt{\left( {{R_{1}\cos \; \varphi_{1}} - {R_{2}\cos \; \varphi_{2}}} \right)^{2} + \left( {{R_{1}\sin \; \varphi_{1}} - {R_{2}\sin \; \varphi_{2}} - t} \right)^{2}}} \\ {{= \sqrt{R_{1}^{2} + R_{2}^{2} - {2\; R_{1}R_{2}{\cos \left( {\varphi_{1} - \varphi_{2}} \right)}} + t^{2} - {2\; {t\left( {{R_{1}\sin \; \varphi_{1}} - {R_{2}\sin \; \varphi_{2}}} \right)}}}},} \end{matrix}$ $M = {\frac{\mu_{0}}{4\pi}{\int_{0}^{2\pi}{\int_{0}^{2\pi}{\frac{R_{1}R_{2}{\cos \left( {\varphi_{1} - \varphi_{2}} \right)}}{\sqrt{R_{1}^{2} + R_{2}^{2} - {2\; R_{1}R_{2}{\cos \left( {\varphi_{1} - \varphi_{2}} \right)}} + t^{2} - {2\; {t\left( {{R_{1}\sin \; \varphi_{1}} - {R_{2}\sin \; \varphi_{2}}} \right)}}}}{\varphi_{1}}\ {{\varphi_{2}}.}}}}}$

The coupling coefficient is calculated numerically and plotted as a function of distance in FIG. 15. The coupling coefficient is already very weak, even when the two loops are side-by-side. When the distance is equal to the radius of loop, the coupling coefficient decreases to less than 0.005.

The above analysis indicates that coupling coefficient for two metallic loops is much weaker in coplanar case than in coaxial case, and decreases rapidly with increasing distance in both cases. The coupling coefficient is proportional to the amount of magnetic flux that can go through the second loop due to the current in the first loop.

As shown in FIG. 14 and FIG. 15, much more flux 1401 of the electromagnetic field goes through the second loop in the coaxial case than in the coplanar case. In wireless power transfer system using inductive coupling or resonant coupling, the receiver (or receivers) is usually arranged in coaxial position with the transmitter instead of coplanar with the transmitter to obtain higher power transfer efficiency and larger transfer distance.

For wireless power transfer based on inductive coupling, a high coupling coefficient (k>0.9) is usually required to achieve high efficiency. Thus, an optimal coaxial alignment and very small distance between transmitter and receiver are required. For wireless power transfer based on resonant coupling, energy can be transferred to receiver via many cycles of resonant exchange of energy between them; efficient power transfer can be achieved even without a high coupling coefficient, as long as the power coupled to the receiver is higher than the power lost in the coupling in each cycle.

Coupling in Array of Resonant Objects

In a wireless energy transfer system using an array of resonant objects according to embodiments of the invention, two or more resonant objects are closely coupled electromagnetically to provide power to receivers. The objects are NOT electrically connected, i.e., the power is transferred only via resonant coupling of electromagnetic waves.

To obtain high transfer efficiency and larger transfer distance, a receiver is preferably arranged such that the axis of its plane is parallel to those of the transmitting objects (coaxial, or coaxial with lateral shift). The resonant objects in the array need to be closely-coupled, to reduce power loss due to coupling. In general, when an array of resonant objects is excited at one end the array, more energy is coupled to the other end of the array when the coupling coefficient between neighboring objects is higher. Moreover, due to the hybridization of resonant coupling, the bandwidth is broader yielding a higher coupling coefficient.

FIG. 16 shows an example of an array of resonant objects 1601 and an energy receiver 1602. The resonant objects are multi-turn resonators. The array has ten such objects arranged in a linear array. The receiver is also a multi-turn resonator, arranged parallel to the array and can move freely along the plane formed by the array. The first object in the array is excited by an external power source. The energy is distributed to all objects of the array via resonant coupling.

As shown in FIG. 17, two different spacing between neighboring objects can be used for the array and the energy transfer efficiency as a function of excitation frequency is calculated by numerical simulations. In case 1, the spacing between neighboring objects is 15% of the width of a resonant object; in case 2, the spacing between neighboring objects is only 3% of the width of a resonant object. The distance between the receiver and the plane of the array is 50% of the width of a resonant object.

The energy transfer efficiency as a function of excitation frequency is shown in FIG. 18. It is seen that the efficiency is higher for all excitation frequencies and the bandwidth is much broader when the array is closely arranged.

Receiver at Different Positions

When a receiving object is at different positions, the coupling between the receiving object and the array is different.

As shown in FIG. 19, the coupling from an array to a receiver is stronger when the receiver is aligned with one object in the array. In comparison, when the receiver is in the middle of neighboring objects, the coupling is weaker; the magnetic flux from the two neighboring objects may have different directions, which cancels out the overall magnetic flux going through the receiving object, and causing the coupling coefficient even smaller.

Due to the change in coupling coefficient, the power transfer efficiency changes correspondingly when the receiving object is at different positions. Moreover, the resonant mode and resonant frequency of the system of the array and the receiver also changes when the receiver changes its location. Working at resonant frequency of the system usually leads to higher power transfer efficiency than working at other frequencies. So, as the receiver moves to different positions different positions, the frequency for peak power transfer efficiency also varies.

FIG. 20 shows a side view of an array of resonant objects and a receiving object traveling along the direction of the array. The system design is shown in FIG. 28. The distance between receiver and the array is 50% the width of a resonant object in the array. The array is excited by an external source at the first object in the array.

The power transfer efficiency as a function of receiver position is shown in FIGS. 21A-21B. The receiver position is in unit of the period of the array; 0 means the receiver is aligned with the first object in the array; the larger the number, the farther away the receiver is from the first object. FIG. 21A and FIG. 21B show plots at two different excitation frequencies. Both Figs. show efficiency fluctuation when the receiver travels along the array. In FIG. 21A, the efficiency varies from 85% to 60%; in FIG. 21B, the efficiency varies from 90% to 10%. The fluctuation is more severe in FIG. 21B than in FIG. 21A, which is due to different resonant modes at the two frequencies.

It is desired to provide ways to reduce the efficiency fluctuation for wireless power transfer using array of resonant objects.

Using Multiple Receivers to Reduce Efficiency Fluctuation in Wireless Power Transfer Using Array of Resonant Objects

Instead of using one resonant object as receiver, two or more objects can be used as receivers. These objects are arranged at different positions and can concurrently move along the array. The energy received at these receivers is then collected and used for power consuming devices. The purpose for using multiple receivers is to offset the efficiency fluctuation and achieve smooth wireless energy transfer when the receivers are at different positions.

FIG. 22 shows an example of an array of resonant objects and two receivers. The first receiver is aligned with one of the resonant object in the array; the second receiver is aligned with the middle of two resonant objects in the array. The distance between receiver and the array is 50% the width of a resonant object in the array. The array is excited by an external source at the first object in the array. The two receivers move simultaneously along the array with no relative movement between them. When the first receiver has a high coupling coefficient, the second receiver has a low coupling coefficient, and vise versa. When the receivers are moving along the array, the power transfer efficiency still fluctuates for each receiver. However, the overall efficiency, which is the ratio of combined power at two receivers and the input power, is stabilized.

FIG. 23A and FIG. 23B show the power transfer efficiency as a function of receiver position at two different frequencies. The receiver position is in unit of the period of the array; 0 means the first receiver is aligned with the first object in the array; the larger the number, the farther away the receivers are from the first object.

In both figures, the efficiency still has strong fluctuation for the two receivers separately; different frequencies have different fluctuations. However, the overall efficiency, due to the use of two receivers, is very much stabilized and higher. In both figures, the overall efficiency fluctuation is within 10%, and the efficiency is above 80% when the receivers are at different positions,

From the example, it is seen that the use of multiple receivers at different positions can reduce the efficiency fluctuation, and maintain high efficiency at different positions significantly. Moreover, it helps to broaden the frequency bandwidth that can be used for wireless power transfer.

Using Multiple Arrays to Reduce Efficiency Fluctuation in Wireless Power Transfer Using Array of Resonant Objects

A combination of more than one array of resonant objects can be used for wireless power transfer to one or more receivers. The different arrays are arranged with offset in position, in order to give a more uniform energy distribution on the path of the receivers than a single array of resonant objects.

FIG. 24 shows an example of two arrays 2401 of resonant objects and a receiving object 2402. The two arrays are closely coupled, with a small distance between them. The resonators in the arrays are arranged with one or more offsets—that is, the upper array is displaced horizontally and/or vertically with respect to the lower array.

As shown in FIG. 25, the EM field is generally stronger near each resonant object in the array. The field is weaker between two resonant objects. Thus, the coupling to a receiving object moving along the array is different at different positions. When two arrays of resonant objects are used, energy is redistributed in the closely coupled arrays.

As shown in FIG. 25, a more uniform distribution pattern is formed at the receiving object. Thus, the coupling to a receiving object is more uniform when the receiving object is at different positions with respect to the array. This reduces fluctuations in the power transfer efficiency.

FIG. 26 shows another example of using two arrays of resonant objects to transmit power wirelessly to one or more receiver. The two arrays are physically separated and may or may not couple to each other. The two arrays can be excited separately by more than one external source. The arrays can also be excited by a single external source and have energy distribution in the arrays via resonant coupling. A receiver 2601 is placed in between two arrays and is coupled to both arrays. The receiver can receive power wirelessly from either array. The arrays can have lateral displacement with respect to each other to achieve a more uniform EM field distribution on the path of the receiver. By using this approach the power transfer to the receiver is more stable with less efficiency fluctuation along the path.

Metamaterials to Enhance Coupling and Improve Power Transfer Efficiency Using Array of Resonant Objects

Metamaterials can be used in wireless power transfer systems. One of the purposes is to improve the power transfer efficiency. Metamaterials can modify the near-field distribution and enhance the coupling of evanescent EM waves. The coupling between a transmitting object (Tx) and a receiving object (Rx) can be improved by a metamaterial. The power transfer efficiency in a wireless power transfer system can be increased by a metamaterial. In previous applications, the use of metamaterials is in a wireless power transfer system using a single object (resonant or non-resonant) as transmitter and a single object (resonant or non-resonant) as receiver. In wireless power transfer system with array of resonant objects, metamaterials can also be used in a similar way.

In FIG. 27, an example of using Metamaterials 2701 for wireless power transfer with array of resonant objects is described. A slab of metamaterial is placed in the middle of an array of resonant objects and a receiving object, and is near the array. The metamaterial can be of different types: double-negative (negative-index metamaterial) or single-negative; different configurations: isotropic or anisotropic. With the metamaterial, the coupling between the array and the receiving object is enhanced; the EM field coupled to the receiving object from the array is increased. Eventually the power transfer efficiency of the system is increased by the metamaterial. This approach is effective when the receiver is moving along the array. The efficiency can be improved when the receiver is at different positions.

In FIG. 28, another example of using metamaterials for wireless power transfer with array of resonant objects is described. A slab of metamaterial is placed in the middle of an array of resonant objects and a receiving object, and is close to the receiving object. Similar to the system in FIG. 27, the coupling between the array and the receiving object is enhanced by the metamaterial; the power transfer efficiency of the system is increased by the metamaterial. This approach is effective when the receiver is moving along the array. The efficiency can be improved when the receiver is at different positions.

Reflectors for EM Shielding and Performance Improvement in a Wireless Power Transfer System Using Array of Resonant Objects

In wireless power transfer system using array of resonant objects, strong EM field exists near the system. On the other hand, coupling to external objects causes extra power loss to the system. It is better to shield the EM field to external environment if possible for safety concerns and system performance. There is also a small part of energy 2901 is lost due to radiation to far field, especially at the termination of arrays, as shown in FIG. 29. Reducing radiation loss can improve the performance of the wireless power transfer system. We describe a device called reflector to do both EM shielding and radiation loss reduction.

The purpose of a reflector is to reduce radiation loss to far field, and shield the system to external environment. The reflector can have different forms. It can be metal sheets, structured metallic sheets, a combination of metallic and dielectric structures, metamaterials, etc. The reflector 3401 can be arranged at the termination of an array, as shown in FIG. 30. The device can also be arranged at other locations, depending on the system configuration and requirements, as shown in FIG. 31.

In FIG. 32, an example is given for system performance with reflectors. Here, a metal box (Faraday cage) is used to cover the system from external environment, such that no radiation can enter. A comparison of efficiency is plotted for a system with an array of resonant objects and a receiver at the same position, with and without the reflector. It is seen from FIG. 32 that a wide band of high power transfer efficiency is obtained with the reflector. The existence of the reflector modifies the resonant coupling behavior of the system, so that the band is shifted compared with the system without reflector.

EFFECT OF THE INVENTION

In prior art, resonator arrays are typically electrically interconnected with each other to form larger composite” resonator. In contrast, the arrays describe herein are electrically isolated. The only coupling is electromagnetic by induction. Furthermore, the energy sink and load can inductively couple to any part of the array because the resonators are strongly coupled.

Although the invention has been described by way of examples of preferred embodiments, it is to be understood that various other adaptations and modifications can be made within the spirit and scope of the invention. Therefore, it is the object of the appended claims to cover all such variations and modifications as come within the true spirit and scope of the invention. 

1. A system for exchanging energy wirelessly, comprising: an array of at least three objects, wherein the objects have similar resonant frequencies, wherein each object is electromagnetic (EM) and non-radiative and generates an EM near-field in response to receiving the energy, wherein each object is electrically isolated from the other objects and arranged at a distance from all other objects, such that upon receiving the energy, the object is strongly coupled to at least one other object via a resonant coupling of evanescent waves; and an energy driver for providing the energy at the resonant frequency to at least one object in the array, such that, during an operation of the system, the energy is distributed from the at least one object to all other objects in the array via the resonant coupling of the evanescent waves.
 2. The system of claim 1, wherein the coupling is inductive, capacitive coupling, or combination thereof.
 3. The system of claim 1, wherein the objects have quality factor greater than
 100. 4. The system of claim 1, wherein the objects in the array are arranged arbitrarily.
 5. The system of claim 1, further comprising: a sink connected to a load, wherein the energy in the array is transferred to the sink via the resonant coupling of the evanescent waves.
 6. The system of claim 4, wherein the sinks moves relative to the array while exchanging the energy.
 7. The system of claim 1, further comprising: a sink connected to a load, wherein the energy in the array is transferred to the sink via the resonant coupling of the evanescent waves.
 8. The system of claim 1, further comprising: a plurality of sinks connected to a load., wherein the energy in the array is transferred to the sink via the resonant coupling of the evanescent waves.
 9. The system of claim 1, further comprising: a plurality of sinks, wherein the sinks are connected to different loads.
 10. The system of claim 1, wherein the objects are arranged in two-dimensions.
 11. The system of claim 1, wherein the objects are arranged in three dimensions.
 12. The system of claim 1, comprising: a plurality of arrays, wherein each array has at least three objects.
 13. The system of claim 13, wherein the arrays are offset from each other.
 14. The system of claim 14, wherein the offset are horizontal, vertical, or combinations thereof.
 15. The system of claim 13, wherein each array is energized independently.
 16. The system of claim 13, wherein the energy in the array is transferred to a single sink.
 17. The system of claim 1, wherein phases and amplitudes of the energy transferred to each object is controlled dynamically.
 18. The system of claim 1, wherein the array includes a metamaterial.
 19. The system of claim 1, wherein the array includes a reflector.
 20. The system of claim 1, further comprising: a Faraday cage enclosing the array.
 21. A system for exchanging energy wirelessly, comprising: an array of at least three objects, wherein the objects have similar resonant frequencies, wherein each object is electromagnetic (EM) and non-radiative and generates an EM near-field in response to receiving the energy, wherein each object is electrically isolated from the other objects and arranged at a distance from all other objects, such that upon receiving the energy, the object is strongly coupled to at least one other object via a resonant coupling of evanescent waves; and an energy driver for providing the energy at the resonant frequency to at least one object in the array, such that, during an operation of the system, the energy is distributed from the at least one object to all other objects in the array via the resonant coupling of the evanescent waves.
 22. A system configured to exchange energy wirelessly, comprising: an energy source comprising a first array of objects; a sink comprising a second array of objects, wherein the objects in the energy source and the sink have similar resonant frequencies, is electromagnetic (EM) and non-radiative, and generates an EM near-field in response to receiving the energy; an energy driver for providing the energy at the resonant frequency to at least one object in the energy source, such that, during an operation of the system, the energy is distributed from the object in the energy source to all other objects in the energy source; and a load for receiving the energy from the sink, wherein the first and the second arrays are strongly coupled to, respectively, at least one other object in the first and the second array, via a resonant coupling of evanescent waves, and wherein the sink is arranged to receive energy wirelessly from the energy source via the resonant coupling of one or many objects in the first array with one or many objects in the second array.
 23. A method for exchanging energy wirelessly, comprising: distributing the energy among all objects in an array of at least three objects, each object has a resonant frequency, is electromagnetic (EM) and non-radiative, and configured to generate an EM near-field in response to receiving the energy, wherein each object in the array is arranged at a distance from all other objects in the array, such that upon receiving the energy the object is strongly coupled to at least one other object in the array via a resonant coupling of evanescent waves, such that, during an operation of the system, the energy is distributed from the object to all other objects in the array; and transmitting the energy wirelessly to a sink arranged at a distance from the array. 